CN104595170A - Air compressor monitoring diagnosis system and method adopting adaptive kernel Gaussian hybrid model - Google Patents

Abstract

The invention discloses an air compressor monitoring diagnosis system and method adopting an adaptive kernel Gaussian hybrid model, and relates to the field of air compressor control technologies. The system comprises a site equipment layer, an equipment control layer and a management and monitoring layer. The site equipment layer is composed of PLCs200, sensors, air compressors, actuators and a water pump, and with the PLCs200 as slave stations, control over the site equipment layer is completed. The equipment control layer comprises an upper computer and a PLC300, with the PLC300 as a master station, the whole air compressor system is controlled through a variable-structure adaptive PID controller based on a support vector machine, and the upper computer monitors the air compressor system. The equipment control layer is in communication with the management and monitoring layer through the industrial Ethernet, and then remote monitoring and data transmission of the upper computer are achieved. The Gaussian hybrid model and the kernel principal component analysis method are integrated in the fault diagnosis method adopted in the upper computer, optimal kernel function parameters are solved through the iterative optimization method, and the purpose of distinguishing different mode data is achieved. The air compressor monitoring diagnosis system and method have higher diagnosis precision and higher practical value.

Description

A kind of air compressor monitoring and diagnosis system and method for self-adaptive kernel gauss hybrid models

Technical field

The present invention relates to air compressor control technique field, specifically a kind of air compressor monitoring and diagnosis system and method for self-adaptive kernel gauss hybrid models.

Background technique

Air compressor is the important main equipment in colliery, is also highly energy-consuming equipment.Along with the application of colliery new process, power equipment and new technology, not only need more air quantity, and require that air compressor can regulate adaptively along with the change of load.And existing outmoded air compressor exists Control platform difference, reliability is low and be difficult to the problems such as real-time monitoring system working state, cause huge energy waste, also bring great burden to operator.Traditional control system adopts distributing manual operation on the spot.During air compressor work, noise is very large, works long hours to bring very large harm to the health of workman, inadequate hommization at this environment.Air compressor uninterrupted operation 24 hours every days needs operator on duty on duty continuously; level of control lowly cause human resources serious waste, and air compressor needs to run continuously, and maintenance period is longer; air compressor service behaviour is unstable, easily occurs the misoperation of warning, shutdown etc.

Concerning mine air compressor, current people also only rest on fault occur after qualitative analysis on, and to the Real-Time Monitoring of air compressor and fault diagnosis also fewer.Overwhelming majority Monitor of Air Compressor just carries out upper and lower inspection to state-variable, judges the working state of air compressor with this.The data of actual acquisition contain much noise, and these noises are difficult to use existing mathematical model to describe, and these class methods are difficult to determine suitable threshold value.Threshold value is crossed conference and is caused being difficult to the slight fault of accurate measurements, the too little meeting of threshold value causes rate of false alarm too high, secondly, due to the very strong coherence between air compressor working procedure variable, and the coherence between variable changes along with the change of operating mode, indivedual variable exceeds threshold value and necessarily breaks down.Again, indivedual variable also necessarily shows that system does not break down in the threshold range of setting, as sensor fault lost efficacy.In recent years, control (MSPC) as Knowledge based engineering multivariate statistics and obtain and develop comparatively widely, and PCA method is a kind of effective ways processing nonautocorrelation between industrial stokehold monitored parameters in MSPC.But PCA method can not monitor the nonlinear organization of input data.The shortcomings such as the monitoring method monitoring accuracy traditional for air compressor is low, and rate of false alarm is high, propose a kind of air compressor monitoring and diagnosis system and method for self-adaptive kernel gauss hybrid models.

Summary of the invention

In order to overcome the shortcoming of above-mentioned prior art, the air compressor monitoring and diagnosis system and method for a kind of self-adaptive kernel gauss hybrid models of the present invention, improve the automaticity of control system of air compressor, far away, the short range that realize air compressor are monitored and Full-automatic monitoring, realize unmanned, and realize air compressor On-line Fault detection and diagnosis.

The present invention realizes with following technological scheme: a kind of air compressor monitoring and diagnosis system of self-adaptive kernel gauss hybrid models, comprises scene equipment level, equipment key-course and management and monitoring layer,

Described scene equipment level adopts PLC200 as substation, PLC200 is connected with voltage for gathering pump motor, electric current, working time, axle temperature, working time after axle temperature, rotor before the voltage of dragging motor, electric current, stator axle temperature, rotor, the sensor of the intake pressure of the pressure in bellows chamber, temperature and air compressor, discharge pressure, entering water temp, water-exit temperature, PLC20 be connected with for control air compressor and water pump open with or close final controlling element;

Described equipment key-course adopts PLC300 as main website, and PLC300 is connected with upper-position unit; PROFIBUS-DP master-slave network is selected to carry out communication between main website and substation, composition distributed I/O system; Main website adopts control unit centered by PLC300, structure-changeable self-adaptive PID controller based on support vector machine controls whole air compressor system, upper-position unit passes through the communication of PROFIBUS-DP protocol realization and main website, the information of each substation is delivered to upper-position unit, realizes the monitoring to whole air compressor system;

Described management and monitoring layer is crossed EPA and is communicated with upper-position unit, realizes remote monitoring and the fault diagnosis of upper-position unit.

It is further: the specific algorithm of the described structure-changeable self-adaptive PID controller based on support vector machine is as follows:

(1) SVM is used to approach nonlinear Control object, and instantaneous linear nonlinear Control object approximate model;

(2) according to departure self-adaptative adjustment PID controller structure;

(3) multi-step prediction thought self-adaptive sites pid parameter is used;

(4) according to the actual pressure signal of feedback and the error of setting pressure signal, calculate controlled quentity controlled variable according to Adaptive PID Control algorithm, realize the control to air compressor system.

Described air compressor system comprises four air compressors, and four air compressors adopt the compound mode of main-auxiliary-standby-maintenance to run, and main process equipment is in closed loop control state all the time.

An air compressor monitoring and diagnosis method for self-adaptive kernel gauss hybrid models, adopt above-mentioned arbitrary monitoring and diagnosis system, concrete steps are as follows:

(1) determine the key variables that fault diagnosis is used, gather air compressor sample data as training sample;

Monitoring parameter used comprises: the voltage of pump motor, electric current, working time; Axle temperature, working time after axle temperature, rotor before the voltage of dragging motor, electric current, stator axle temperature, rotor; Pressure in bellows chamber, temperature; The intake pressure of air compressor, discharge pressure, entering water temp, water-exit temperature;

(2) being normalized collecting collection air compressor sample data, data being removed the impact of dimension;

(3) in low n-dimensional subspace n, GMM is used to disclose data to cluster data multi-modal;

(4) then according to data multi-modal information, the kernel functional parameter algorithm for estimating based on entropy is utilized to find local optimum kernel functional parameter in original data space;

(5) local optimum kernel functional parameter is utilized to use KPCA that non-linear higher-dimension multi-modal data set transformation low-dimensional is differentiated subspace, if algorithm does not reach end condition, then forward the first step to and continue iteration execution, complete the fault diagnosis to air compressor system by self-adaptive kernel gauss hybrid models.

The invention has the beneficial effects as follows: the automaticity improving control system of air compressor, far away, the short range that realize air compressor are monitored and Full-automatic monitoring, realize unmanned, and realize air compressor On-line Fault detection and diagnosis.

Accompanying drawing explanation

Fig. 1 is the centralized control system structural drawing based on PLC of the present invention;

Fig. 2 is the structure-changeable self-adaptive PID control system schematic diagram based on SVM of the present invention;

Fig. 3 is the key character parameter source schematic diagram of pressure fan fault diagnosis system of the present invention;

Fig. 4 is the air compressor method for diagnosing faults flow chart of a kind of self-adaptive kernel gauss hybrid models of the present invention.

Embodiment

As depicted in figs. 1 and 2, a kind of air compressor monitoring and diagnosis system of self-adaptive kernel gauss hybrid models, comprise scene equipment level, equipment key-course and management and monitoring layer, described scene equipment level is by PLC200, sensor, air compressor, final controlling element and water pump are formed, using PLC200 as substation, complete the control to scene equipment level, described equipment key-course comprises upper-position unit and PLC300, using PLC300 as main website, PROFIBUS-DP master-slave network is selected to carry out communication between main website and 5 slave stations, composition distributed I/O system, the input signal of slave station can be sent to main website rapidly, the instruction that main website sends and Output rusults also can be sent to slave station in time and perform output, adopt control unit centered by PLC, structure-changeable self-adaptive PID controller based on support vector machine (SVM) controls whole air compressor system, upper-position unit adopts Siemens WinCC software, this software passes through the communication of PROFIBUS-DP protocol realization and main website, the information of each substation is delivered to upper-position unit, realize the monitoring to whole air compressor system, equipment key-course is communicated by EPA with management and monitoring layer, thus realizes remote monitoring and the fault diagnosis of upper-position unit 3, and the method for system fault diagnosis adopts self-adaptive kernel gauss hybrid models.

Air compressor system is control unit centered by PLC300, uses SVM on-line identification Controlling model, Automatic adjusument pid parameter, ensure that pid control algorithm works in the optimum state, regulate air compressor working load adaptively, reach the object of constant pressure air feeding, improve stability and the robustness of system; Air compressor realizes startup, stopping, loading and unloading condition by frequency conversion soft start and changes; Four air compressors adopt the compound mode of main-auxiliary-standby-maintenance to run, main process equipment is in closed loop control state all the time, according to the actual pressure signal of feedback and the error of setting pressure signal, controlled quentity controlled variable is calculated according to Adaptive PID Control algorithm, according to the compressed air line force value monitored, make decisions on one's own and control the start-stop of on-the-spot air compressor, control system can realize automatically to the Stress control of main line, realizes unattended operation.

Algorithm principle based on the structure-changeable self-adaptive PID controller of support vector machine is as follows:

(1) SVM is used to approach nonlinear Control object, and instantaneous linear non-linear object approximate model;

(2) according to departure self-adaptative adjustment PID controller structure;

(3) multi-step prediction thought self-adaptive sites pid parameter is used;

(4) according to the actual pressure signal of feedback and the error of setting pressure signal, calculate controlled quentity controlled variable according to Adaptive PID Control algorithm, and then realize the control to air compressor system.

Upper-position unit 3 adopts Siemens WinCC software, to 5 substation Real-Time Monitoring running statees, provides indicating fault and warning simultaneously; The telecontrol of air compressor can be realized in interface, operating mode switches, fault is checked and the inquiry of air compressor and water pump operation state; The setting of alarm parameters can be carried out simultaneously at monitoring interface, the link of real time data inquiry, in real time form, warning inquiry etc. is provided, the individual functions such as inquiry form, real time data, warning can be switched fast, show out of order place more intuitively; And the faults such as the power failure in system cloud gray model, air compressor off-grid, power failure, total snorkel overpressure or too low, cooling water pressure is too low, pipeline overtemperature are monitored in real time, send alarm in time.

As Fig. 3, based on the method for diagnosing faults of self-adaptive kernel gauss hybrid models, adopt the monitoring and diagnosis system in Fig. 1, concrete steps are as follows:

(1) determine the key variables that fault diagnosis is used, gather air compressor sample data as training sample;

Monitoring parameter used comprises: the voltage of pump motor, electric current, working time; Axle temperature, working time after axle temperature, rotor before the voltage of dragging motor, electric current, stator axle temperature, rotor; Pressure in bellows chamber, temperature; The intake pressure of air compressor, discharge pressure, entering water temp, water-exit temperature;

(2) be normalized collecting collection air compressor sample data, concrete steps are as follows:

21) in low n-dimensional subspace n, GMM is used to disclose data to cluster data multi-modal;

22) then according to data multi-modal information, the kernel functional parameter algorithm for estimating based on entropy is utilized to find local optimum kernel functional parameter in original data space;

23) local optimum kernel functional parameter is utilized to use KPCA that non-linear higher-dimension multi-modal data set transformation low-dimensional is differentiated subspace, if algorithm does not reach end condition, then forward the first step to and continue iteration execution, by completing the fault diagnosis to air compressor system based on the self-adaptive kernel gauss hybrid models of entropy, there is important scientific research value and engineer applied is worth.

The object of self-adaptive kernel gauss hybrid models carries out cluster to low-dimensional Reduced Data Set exactly in lower dimensional space.For high dimension sparse data collection, GMM clustering algorithm is often subject to the unusual problem of composition covariance matrix.How finding the compactedness that low n-dimensional subspace n improves degree of separation between data modality and mode inside, is the key determining GMM algorithm performance.KPCA just retains the covariance information of original High Dimensional Data Set, the DATA POPULATION geometry information that low n-dimensional subspace n can only reflect, cannot disclose the geometry authentication information that File is implicit.And making full use of File, to imply authentication information be the key improving GMM performance.Suitable KPCA kernel functional parameter how is selected to be the key improving the mode authentication information ability that KPCA extracted data collection implies.Self-adaptive kernel gauss hybrid models performs KPCA to high dimensional data Dimensionality Reduction and GMM clustering algorithm by iteration.The data authentication information wherein utilizing GMM cluster result to obtain obtains the optimum kernel functional parameter of KPCA, thus in low-dimensional yojan subspace, maintain the discriminating geological information of data, also improves the data clusters performance of GMM at lower dimensional space conversely.Like this, optimum kernel functional parameter value and Clustering Effect is finally asked for by above-mentioned iterative optimization procedure.As shown in Figure 4, adopt the self-adaptive kernel gauss hybrid models of entropy to carry out fault diagnosis and prediction to compressor operation state, step is as follows:

1, gauss hybrid models and computational process:

Gauss hybrid models can be expressed as by the weighted sum of multiple single Gaussian component

$p\left(x\right|\mathrm{\Θ})=\underset{i=1}{\overset{N_k}{\mathrm{\Σ}}}{\mathrm{\π}}_{i}p\left(x\right|{\mathrm{\θ}}_i)---\left(1\right)$

Wherein, π _ibe hybrid parameter and meet θ _ibe the parameter of i-th gauss component, make X=[x ₁, x ₂..., x _n] be the parameter training sample of training data set compressor operation feature, suppose x _iindependent sample from mixed distribution, our target finds Θ to make likelihood function p (X| Θ) maximum.The optimization problem that such hybrid model is corresponding can be written as

$L\left(\mathrm{\Θ}\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\log \underset{j=1}{\overset{N_k}{\mathrm{\Σ}}}{\mathrm{\π}}_j{p}_j\left(x\right|{\mathrm{\θ}}_j)---\left(2\right)$

$s.t.\underset{i=1}{\overset{N_k}{\mathrm{\Σ}}}{\mathrm{\π}}_i=1$

Above-mentioned optimization is non-convex optimization problem, in order to simplify above-mentioned likelihood representation, introduces implicit indicator variable z _ij∈ { 0,1}, and z _ij=1.Represent x _isample in distributed component j, on the contrary then z _ij=0;

So p (Z| Θ) is expressed as

$p\left(Z\right|\mathrm{\Θ})=\underset{i=1}{\overset{N}{\mathrm{\Π}}}p\left(z_i\right|\mathrm{\Θ})=\underset{i=1}{\overset{N}{\mathrm{\Π}}}\underset{j=1}{\overset{N_k}{\mathrm{\Π}}}{{\mathrm{\π}}_j}^{z_{\mathrm{ij}}}---\left(3\right)$

About Θ and condition distribution likelihood function become

$p\left(X\right|\mathrm{\Θ},Z)=\underset{i=1}{\overset{N}{\mathrm{\Π}}}\underset{j=1}{\overset{N_k}{\mathrm{\Π}}}p{\left(x_i\right|{\mathrm{\θ}}_j)}^{z_{\mathrm{ij}}}---\left(4\right)$

Therefore, the complete likelihood function of logarithm becomes

$L\left(\mathrm{\Θ}\right)=\log p(X,Z|\mathrm{\Θ})=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_k}{\mathrm{\Σ}}}{z}_{\mathrm{ij}}\log {\mathrm{\π}}_{j}p\left(x_i\right|{\mathrm{\θ}}_j)---\left(5\right)$

2, the self adaption that the present invention proposes solves optimized parameter N _iprocess:

Optimized parameter can be asked for by methods such as expectation-maximization algorithm.High-order statistic skewness and kurtosis can measure the training data [] of Gaussian Mixture Model Probability Density matching certain kinds.Make N _ibe the training data quantity of the i-th composition, with be respectively statistic skewness and kurtosis that i-th composition tie up about d, it is calculated as follows

${\hat{s}}_{i,d}=\frac{\frac{1}{N_i}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{h}_i^n{(x_{\mathrm{id}}^n-{\widehat{\mathrm{\μ}}}_{\mathrm{id}})}^3}{{\widehat{\mathrm{\σ}}}_{\mathrm{id}}^3}---\left(6\right)$

${\hat{k}}_{i,d}=\frac{\frac{1}{N_i}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{h}_i^n{(x_{\mathrm{id}}^n-{\widehat{\mathrm{\μ}}}_{\mathrm{id}})}^4}{{\widehat{\mathrm{\σ}}}_{\mathrm{id}}^4}---\left(7\right)$

Wherein, be belong to the posterior probability of the i-th composition, with the average that i-th composition is tieed up about d and standard deviation.The distribution tieed up about d when i-th composition is Gaussian distribution, Skewness and kurtosis estimates to approach 0, otherwise high-order statistic departs from 0.And may be calculated about skewness and the kurtosis distribution of component i

${\hat{s}}_i=\frac{1}{D}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}\left|{\hat{s}}_{i,d}\right|---\left(8\right)$

${\hat{k}}_i=\frac{1}{D}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}\left|{\hat{k}}_{i,d}\right|---\left(9\right)$

Non-Gaussian system about GMM can be defined as

$\mathrm{\Φ}=\underset{c=1}{\overset{C}{\mathrm{\Σ}}}{\mathrm{\π}}_c({\hat{s}}_c+{\hat{k}}_c)---\left(10\right)$

This tolerance estimates the degree of GMM to the fitting of distribution of training data essence, uses the composition that criterion below selects degree of fitting the poorest

$c^{*}=\underset{c}{\arg \max }{\mathrm{\π}}_c({\hat{s}}_c+{\hat{k}}_c)---\left(11\right)$

Suppose that c composition non-Gaussian system is maximum, use literary composition [] non-negative to divide this composition, new composition parameter is initialized as Φ={ Θ _k1, Θ _k2.Fission process is []

$a_{c_1}=u_1{a}_{c^{*}}---\left(12\right)$

$a_{c_2}=(1-u_1)a_{c^{*}}---\left(13\right)$

${\mathrm{\μ}}_{c_1}={\mathrm{\μ}}_{c^{*}}-\left(\underset{i=1}{\overset{d}{\mathrm{\Σ}}}{u}_2^i\sqrt{{\mathrm{\λ}}_{c^{*}}^i}{v}_{c^{*}}^i\right)\sqrt{\frac{a_{c_1}}{a_{c_2}}}---\left(14\right)$

${\mathrm{\μ}}_{c_2}={\mathrm{\μ}}_{c^{*}}+\left(\underset{i=1}{\overset{d}{\mathrm{\Σ}}}{u}_2^i\sqrt{{\mathrm{\λ}}_{c^{*}}^i}{v}_{c^{*}}^i\right)\sqrt{\frac{a_{c_1}}{a_{c_2}}}---\left(15\right)$

${\mathrm{\Λ}}_1=\mathrm{diag}\left(u3\right)\mathrm{diag}(\mathrm{\ι}-u2)\mathrm{diag}(\mathrm{\ι}+u2){\mathrm{\Λ}}_{*}\frac{a_{c^{*}}}{a_{c_1}}---\left(16\right)$

${\mathrm{\Λ}}_2=\mathrm{diag}(\mathrm{\ι}-u3)\mathrm{diag}(\mathrm{\ι}-u2)\mathrm{diag}(\mathrm{\ι}+u2){\mathrm{\Λ}}_{*}\frac{a_{c^{*}}}{a_{c_2}}---\left(17\right)$

$V_1=D{V}_{c^{*}}---\left(18\right)$

$V_2=D^T{V}_{c^{*}}---\left(19\right)$

Here with matrix respectively ascending order eigenvalue and characteristic of correspondence vector. be diagonal matrix, D represents D × D spin matrix, and each of matrix is classified as orthonormal vector.This matrix by D (D-1)/2 difference meet the Dynamic data exchange real estate being uniformly distributed U (0,1) give birth to triangular matrix set up.ι to be element be entirely 1 D × 1 vector, with represent 2D+1 stochastic variable, they are by method generation below

$u_1~\mathrm{Beta}\left(\mathrm{2,2}\right),u_2^1~\mathrm{Beta}\left(\mathrm{1,2}D\right),u_3^1~\mathrm{Beta}(1,D)---\left(20\right)$

$u_2^j~U(-\mathrm{1,1})\mathrm{and}{u}_3^j~U\left(\mathrm{0,1}\right)\mathrm{with\; j}=\mathrm{2,3},...,D---\left(21\right)$

Here Beta () is beta distribution.

What 3, the present invention proposed solves optimized parameter σ and w _dparametric procedure:

The maximum advantage of core pivot element analysis (KPCA) allows us to use a mercer kernel function to calculate dot product on higher dimensional space.Therefore, without the need to the projected forms from the data projection of the input space to higher dimensional space, and effectively describe the nonlinear organization of data.KPCA method is a kind of effective preprocess method of Multi task, causes extensive concern because its physical significance is simple, be convenient to the advantages such as application.

Particularly, given N number of training sample x ₁, x ₂..., x _nφ: x → φ (x) ∈ H is made to be Nonlinear Mapping from the input space to high-dimensional feature space H, use and reproducing kernel Hilbert space (Reproducing Kernel Hilbert Space, RKHS) inner product in relevant kernel function calculated characteristics space H, it is expressed as k (x, x ')=φ (x) ^tφ (x ').Two kinds of conventional kernel functions are Polynomial kernel function and Gaussian Radial basis kernel function, and its definition is respectively

$k(x_i,x_j)={(x_j^T{x}_i+1)}^d---\left(22\right)$

$k(x_i,x_j)=\exp (-\frac{{\left|\right|x_j-x_i\left|\right|}^2}{\mathrm{\γ}}),\mathrm{\γ}\∈R^{+}---\left(23\right)$

The average of the mapped sample of feature space is calculated as by following formula

$\stackrel{\‾}{\mathrm{\φ}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\φ}\left(x_i\right)=\mathrm{\ΦS}---\left(24\right)$

Here Φ=[φ (x ₁), φ (x ₂) ..., φ (x _n)], S=1 _n/ N, 1 _nrepresent that whole element is N × 1 vector of 1.In feature space, the centralize method of sample is

$\widehat{\mathrm{\φ}}\left(x_i\right)=\mathrm{\φ}\left(x_1\right)-\stackrel{\‾}{\mathrm{\φ}},i=\mathrm{1,2},...,N---\left(25\right)$

So, by the centralization nuclear matrix of the covariance matrix in following formula construction feature space be

$\stackrel{\‾}{K}=K-\frac{1}{N}{1}_{\mathrm{NN}}K-\frac{1}{N}K{1}_{\mathrm{NN}}+\frac{1}{N^2}{1}_{\mathrm{NN}}K{1}_{\mathrm{NN}}---\left(26\right)$

Wherein, 1 _nNrepresent the unit matrix of N × N, (i, j) individual element of centralization nuclear matrix function is $\stackrel{\‾}{k}(x_i,x_j)=\stackrel{\‾}{k}(x_i,x_j)-\frac{1}{N}{1}_{1N}{k}_{x_i}-\frac{1}{N}{1}_{1N}{k}_{x_j}+\frac{1}{N^2}{1}_{1N}K{1}_{N1},$ $k_{x_i}={[k(x_i,x_1),k(x_i,x_2),...,k(x_i,x_N)]}^T$ With K=[k (x _i, x _j)] _{i, j=1,2 ..., N}.Because kernel function is symmetrical, continuous and positive definite, so matrix K is also symmetrical and positive semi-definite.The eigenvalue problem that KPCA is expressed from the next is asked for, namely

$\stackrel{\‾}{K}{\mathrm{\α}}_i={\mathrm{\λ}}_i{\mathrm{\α}}_i---\left(27\right)$

Here λ _ibe i-th eigenvalue of maximum, α _ifor corresponding λ _icharacteristic vector.Be the characteristic vector of the covariance matrix of feature space due to each composition, each composition is opened into by training sample, and its corresponding coefficient is the coordinate of α.Therefore mapped sample project to i-th composition v _iprovided by following formula

${\mathrm{\β}}_i=\stackrel{\‾}{\mathrm{\φ}}{\left(x\right)}^T{v}_i=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_{\mathrm{in}}k(x,x_n)={\mathrm{\α}}_i^T{\stackrel{\‾}{k}}_x---\left(28\right)$

Suppose, use matrix d composition corresponding to d eigenvalue of maximum carry out Dimensionality Reduction, projective representation after d composition is

$P_d\left(x\right)={[{\mathrm{\α}}_1,{\mathrm{\α}}_2,...,{\mathrm{\α}}_d]}^T{\stackrel{\‾}{k}}_x=A^T{\stackrel{\‾}{k}}_x---\left(29\right)$

Here A=[α ₁, α ₂..., α _d]. in actual applications, the superior function of KPCA depends on kernel functional parameter.Conventional KPCA model parameter and scale parameter to be the effect of a positive number be control nuclear mapping non-linear, and equalization treats each variable.But different variable is different to the effect disclosing data structure in low n-dimensional subspace n, therefore only uses single scale parameter inadequate often.For this reason, the modified model gaussian kernel function that this invention proposes is

$k(x,y)=\exp \left(\frac{{(x-y)}^{T}W(x-y)}{2}\right)=\exp (-\frac{1}{2{\mathrm{\σ}}^2}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_d{(x_d-y_d)}^2)---\left(30\right)$

To great majority supervision and semi-supervised learning method, use and must connect (ML) and can not be connected (CL).The supervision message of constraint representation effectively can improve the performance of learning algorithm.Wherein, ML constraint representation two observation samples must belong to identical cluster or classification, and CL constraint is specified and do not belonged to two similar Observed values.

Make φ: x → φ (x) ∈ H be Nonlinear Mapping geometry from the input space to high-dimensional feature space H, the dot product of space H is by being defined as k (x, x ')=φ (x) ^tthe Mercer kernel function of φ (x ') calculates.Conventional gaussian kernel function is defined as the gaussian kernel function that the present invention adopts is defined as

$k(x,y)=\exp \left(\frac{{(x-y)}^{T}W(x-y)}{2}\right)=\exp (-\frac{1}{2{\mathrm{\σ}}^2}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_d{(x_d-y_d)}^2)---\left(31\right)$

Here W=σ ^-2diag (w ₁, w ₂..., w _d) .w _dfor the weight that data d ties up.From the viewpoint of theory of probability, w _dthe probability that d dimension data is contributed File can be regarded as, thus can be regarded as dimension weight.

Provide ML and CL, optimum kernel functional parameter can be asked for by using CL and ML.Optimization problem can be defined as

$\min L(W,{\mathrm{\σ}}^2)=-\underset{(x_i,x_j)\∈\mathrm{ML}}{\mathrm{\Σ}}{\left|\right|\mathrm{\φ}\left(x_i\right)-\mathrm{\φ}\left(x_j\right)\left|\right|}^2+\underset{(x_i,x_j)\∈\mathrm{CL}}{\mathrm{\Σ}}{\left|\right|\mathrm{\φ}\left(x_i\right)-\mathrm{\φ}\left(x_j\right)\left|\right|}^2+\mathrm{\η}\underset{i=1}{\overset{D}{\mathrm{\Σ}}}{w}_i\ln w_i---\left(32\right)$

$s.t.\underset{i=1}{\overset{D}{\mathrm{\Σ}}}{w}_i=\mathrm{1,0}\≤w_i\≤1---\left(33\right)$

Minimize be equivalent to similarity between the cluster between maximization cluster and other clusters, minimize the similar degree in the class of cluster simultaneously. last term use objective function about dimension weight as regularization term, object is for avoiding the over-fitting problem of cluster process.Positive parameter γ controls the compromise between similar degree in the class and class between similarity.In objective function, the object of regularization term makes more dimension identification cluster, solves the problem that sparse data clustering only uses a small amount of dimension cluster.Therefore, when there is redundancy feature, portraying openness optimization problem is explicit, improving KPCA performance preferably.This strategy of place better solves cluster higher-dimension, sparse data problem.

Use geo-nuclear tracin4 and abandon the constant term not affecting final optimization pass result, above-mentioned optimization problem can transform the following optimization problem of literary composition

$\min J(W,{\mathrm{\σ}}^2)=-\underset{(x_i,x_j)\∈\mathrm{CL}}{\mathrm{\Σ}}k(x_i,x_j)-\underset{(x_i,x_j)\∈\mathrm{ML}}{\mathrm{\Σ}}k(x_i,x_j)+\mathrm{\η}\underset{i=1}{\overset{D}{\mathrm{\Σ}}}{w}_i\ln w_i---\left(34\right)$

$s.t.\underset{i=1}{\overset{D}{\mathrm{\Σ}}}{w}_i=1---\left(35\right)$

About w _iand σ ²optimal solution do not try to achieve by the above-mentioned optimization problem of direct solution.Here existing many Multiplier Methods are adopted to solve above-mentioned optimization problem.Lagrange multiplier function corresponding to above-mentioned optimization problem can be written as

$L(W,{\mathrm{\σ}}^2,\mathrm{\λ})=J(W,{\mathrm{\σ}}^2)-\mathrm{\λ}(\underset{i=1}{\overset{D}{\mathrm{\Σ}}}{w}_i-1)---\left(36\right)$

Broad object function W, σ ², δ and λ ^*can be expressed as at following formula respectively

$\arg \min M(W,{\mathrm{\σ}}^2,\mathrm{\δ},\mathrm{\λ})=L(W,{\mathrm{\σ}}^2,\mathrm{\λ})+\frac{\mathrm{\δ}}{2}{(\underset{i=1}{\overset{D}{\mathrm{\Σ}}}{w}_i-1)}^2---\left(37\right)$

In order to calculate above-mentioned unconstrained optimization problem, under the condition of fixing λ and δ, calculate W and σ with gradient descent algorithm ², computational process is as follows:

$\frac{\∂M}{\∂\mathrm{\σ}}=\frac{\∂J}{\∂\mathrm{\σ}}=\underset{(x_i,x_j)\∈\mathrm{CL}}{\mathrm{\Σ}}\frac{\∂k(x_i,x_j)}{\∂\mathrm{\σ}}-\underset{(x_i,x_j)\∈\mathrm{ML}}{\mathrm{\Σ}}\frac{\∂k(x_i,x_j)}{\∂\mathrm{\σ}}---\left(38\right)$

$\frac{\∂M}{\∂w_i}=\frac{\∂L}{\∂w_i}+\mathrm{\δ}(\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_d-1)---\left(39\right)$

In formula,

$\frac{\∂k(x_i,x_j)}{\∂\mathrm{\σ}}=\left(\frac{1}{{\mathrm{\σ}}^3}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_d{(x_d-y_d)}^2\right)\exp (-\frac{1}{2{\mathrm{\σ}}^2}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_d{(x_d-y_d)}^2)---\left(40\right)$

$\frac{\∂L}{\∂w_i}=\underset{(x_i,x_j)\∈\mathrm{CL}}{\mathrm{\Σ}}\frac{\∂k(x_i,x_j)}{\∂w_i}-\underset{(x_i,x_j)\∈\mathrm{ML}}{\mathrm{\Σ}}\frac{\∂k(x_i,x_j)}{\∂w_i}+1+\ln w_i-\mathrm{\λ}---\left(38\right)$

$\frac{\∂k(x_i,x_j)}{\∂w_i}=-\frac{1}{2{\mathrm{\σ}}^2}{(x_i-y_i)}^2\exp (-\frac{1}{2{\mathrm{\σ}}^2}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_d{(x_d-y_d)}^2)---\left(42\right)$

Therefore, can obtain

$\mathrm{\σ}(t+1)=\mathrm{\σ}\left(t\right)-\mathrm{\ρ}\frac{\∂M}{\∂\mathrm{\σ}}|\mathrm{\σ}=\mathrm{\σ}\left(t\right)---\left(43\right)$

$w_i(t+1)=w_i\left(t\right)-\mathrm{\ρ}\frac{\∂M}{\∂w_i}|w_i=w_i\left(t\right)---\left(44\right)$

In formula, one step parameter ρ can be obtained by existing searching algorithm.Utilize gradient descent algorithm can ensure local parameter σ and w _doptimum.

$\mathrm{\λ}(t+1)=\mathrm{\λ}\left(t\right)-\mathrm{\δ}(\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_d-1)---\left(45\right)$

$\mathrm{\δ}(t+1)=\left\{\begin{array}{cc}{c}^{\′}\mathrm{\δ}\left(t\right),& \mathrm{if}|\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_d\left(t\right)-1|/|\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_d(t-1)-1|>{\mathrm{\ϵ}}^{\mathrm{\δ}}\\ \mathrm{\δ}\left(t\right),& \mathrm{otherwise}\end{array}\right.---\left(46\right)$

In formula, c ' > 1 represents power gain, ε ^δ∈ (0,1). these parameter W, σ ², λ, δ are upgraded until reach end condition by iteration the details that multiplication is optimized can with reference to [].

4, the Testing index of pressure fan is set up

Based on the monitoring of equipment method of GMM, first estimate the parameter of EKAGMM according to training data, and calculate the posterior probability of Monitoring Data to each gauss component (or cluster).Then calculate overall situation monitoring reasoning index according to Local Posteriori Probability and carry out faut detection.Sample x _iconditional probability density function be expressed as

$p\left(x_i\right|w_c,o_c,{\mathrm{\σ}}_c^2)={\left(\underset{d=1}{\overset{D}{\mathrm{\Π}}}\frac{w_{\mathrm{cd}}}{2\mathrm{\π}{\mathrm{\σ}}_c^2}\right)}^{-\frac{1}{2}}\exp (-\frac{1}{2{\mathrm{\σ}}_c^2}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_{\mathrm{td}}\left({(x_{\mathrm{id}}-o_{\mathrm{cd}})}^2\right))---\left(47\right)$

According to bayesian criterion, sample x _iposterior probability can be calculated by following formula

$p\left(c\right|x)=\frac{a_c\left(\underset{d=1}{\overset{D}{\mathrm{\Π}}}\sqrt{\frac{w_{\mathrm{cd}}}{{\mathrm{\σ}}_c^2}}\right)\exp (-\frac{1}{2{\mathrm{\σ}}_c^2}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_{\mathrm{cd}}\left({(x_{\mathrm{id}}-o_{\mathrm{cd}})}^2\right))}{\underset{t=1}{\overset{C}{\mathrm{\Σ}}}\left(\underset{d=1}{\overset{D}{\mathrm{\Π}}}\sqrt{\frac{w_{\mathrm{cd}}}{{\mathrm{\σ}}_t^2}}\right)\exp (-\frac{1}{2{\mathrm{\σ}}_t^2}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_{\mathrm{td}})\left({(x_{\mathrm{id}}-o_{\mathrm{cd}})}^2\right)}---\left(48\right)$

Suppose that each gauss component obeys single mode Gaussian distribution, so to sample the sample x obtained from a gauss component _tmahalanobis distance (MD) obey distribution. represent sample x _iwith gauss component MD square, degrees of freedom D equals input amendment is here dimension, $D_{\mathrm{local}}^c\left(x_i\right)={(x_i-o_c)}^T{\mathrm{\Σ}}_c^{-1}(x_i-o_c)=\frac{1}{{\mathrm{\σ}}_c^2}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_{\mathrm{cd}}\left({(x_{\mathrm{id}}-o_{\mathrm{cd}})}^2\right).$ The probability that monitor sample based on local MD belongs to each cluster can be estimated by following formula

$p^{\left(c\right)}\left(x_t\right)=\mathrm{Pr}\{\left(D_{\mathrm{local}}^c\left(x\right)\right|x\∈{\mathrm{\Θ}}_c)\≤\left(D_{\mathrm{local}}^c\left(x_t\right)\right|x_t\∈{\mathrm{\Θ}}_c)\}---\left(49\right)$

P ^(c)(x _t) also can by the χ with suitable degrees of freedom ²probability density function calculates, and it represents sample x _tbelong to composition Θ _cprobability.Be similar to the reasoning monitoring and statistics amount construction method based on Bayesian reasoning, the reasoning monitoring and statistics amount (EAKGMMIMS) based on EAKGMM is set up by following formula

$\begin{array}{c}\mathrm{EAKGMMIMS}\left(x_t\right)=\underset{c=1}{\overset{C}{\mathrm{\Σ}}}{p}^{\left(c\right)}\left(x_t\right)p\left(c\right|x_t)\\ =\underset{c=1}{\overset{C}{\mathrm{\Σ}}}{p}^{\left(c\right)}\left(x_t\right)\frac{a_c\left(\underset{d=1}{\overset{D}{\mathrm{\Π}}}\sqrt{\frac{w_{\mathrm{cd}}}{{\mathrm{\σ}}_c^2}}\right)\exp (-\frac{1}{2{\mathrm{\σ}}_c^2}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_{\mathrm{cd}}\left({(x_{\mathrm{id}}-o_{\mathrm{cd}})}^2\right))}{\underset{t=1}{\overset{C}{\mathrm{\Σ}}}\left(\underset{d=1}{\overset{D}{\mathrm{\Π}}}\sqrt{\frac{w_{\mathrm{cd}}}{{\mathrm{\σ}}_t^2}}\right)\exp (-\frac{1}{2{\mathrm{\σ}}_t^2}\underset{d=1}{\overset{D}{\mathrm{\Σ}}}{w}_{\mathrm{td}}\left({(x_{\mathrm{id}}-o_{\mathrm{cd}})}^2\right))}\end{array}---\left(50\right)$

Overall situation monitoring and statistics amount utilizes the posterior probability of all gauss components, represents the probability of observation sample in normal state.Due to without the need to determining monitor sample x _tthe single gauss component belonged to, overall monitoring and statistics figureofmerit can avoid the potential risk of the mistake monitoring caused by misclassification.Due to p ^(c)(x _t) and p (c|x _t) be all less than 1, be easy to known EAKGMMIMS (x _t) be also less than 1. and therefore whether can exceed (1-a) 100% determining apparatus state whether normal or fault state by EAKGMMIMS.

6, fault diagnosis and classification

The method can determine its source of trouble by the contribution rate comparing each monitored parameters.In c class, d monitored variable is passed through first-order partial derivative by estimation

$C_{D_c}^{\left(d\right)}\left(x\right)=\frac{\∂D_{\mathrm{local}}^c\left(x\right)}{\∂x_d}=\frac{2}{{\mathrm{\σ}}_c^2}{w}_{\mathrm{cd}}\left((x_{\mathrm{id}}-o_{\mathrm{cd}})\right)---\left(51\right)$

Then, total contribution rate of the d dimension monitored parameters of EEGMMIMS can be obtained by following formula

$C_{\mathrm{EAKGMMIMS}}^{\left(d\right)}\left(x\right)=\underset{c=1}{\overset{C}{\mathrm{\Σ}}}{p}^{\left(c\right)}\left(x\right)C_{D_c}^{\left(d\right)}\left(x\right)---\left(52\right)$

The significant level a of upper control limits can be obtained by following formula

$\mathrm{DL}=\frac{D(N-1)}{N-D}{F}_{D,N-D,a}---\left(53\right)$

Therefore, tolerance obeys approximate χ ²distribution.

The present invention can follow the tracks of the force value of setting preferably, solves the problem of air compressor load wide variation, improves control accuracy, has good robust performance; Overcome existing air compressor monitoring algorithm and consider coherence between variable very well and the problem that causes rate of false alarm too high, and adapt to equipment multi-operating mode monitoring running state.Have employed, based on self-adaptive kernel gauss hybrid models, real-time monitoring and diagnosis is carried out to operation troubles, there is higher diagnostic accuracy.

Claims (4)

1. an air compressor monitoring and diagnosis system for self-adaptive kernel gauss hybrid models, comprises scene equipment level, equipment key-course and management and monitoring layer, it is characterized in that:

Described scene equipment level adopts PLC200 as substation, PLC200 is connected with voltage for gathering pump motor, electric current, working time, axle temperature, working time after axle temperature, rotor before the voltage of dragging motor, electric current, stator axle temperature, rotor, the sensor of the intake pressure of the pressure in bellows chamber, temperature and air compressor, discharge pressure, entering water temp, water-exit temperature, PLC200 be connected with for control air compressor and water pump open with or close final controlling element;

Described equipment key-course adopts PLC300 as main website, and PLC300 is connected with upper-position unit; PROFIBUS-DP master-slave network is selected to carry out communication between main website and substation, composition distributed I/O system; Main website adopts control unit centered by PLC300, structure-changeable self-adaptive PID controller based on support vector machine controls whole air compressor system, upper-position unit passes through the communication of PROFIBUS-DP protocol realization and main website, the information of each substation is delivered to upper-position unit, realizes the monitoring to whole air compressor system;

Described management and monitoring layer is communicated with upper-position unit by EPA, realizes remote monitoring and the fault diagnosis of upper-position unit.

2. want the air compressor monitoring and diagnosis system of a kind of self-adaptive kernel gauss hybrid models described in ball 1 according to right, it is characterized in that: the specific algorithm of the described structure-changeable self-adaptive PID controller based on support vector machine is as follows:

(1) SVM is used to approach nonlinear Control object, and instantaneous linear nonlinear Control object approximate model;

(2) according to departure self-adaptative adjustment PID controller structure;

(3) multi-step prediction thought self-adaptive sites pid parameter is used;

(4) according to the actual pressure signal of feedback and the error of setting pressure signal, calculate controlled quentity controlled variable according to Adaptive PID Control algorithm, realize the control to air compressor system.

3. the air compressor monitoring and diagnosis system of a kind of self-adaptive kernel gauss hybrid models described in ball 1 or 2 is wanted according to right, it is characterized in that: described air compressor system comprises four air compressors, four air compressors adopt the compound mode of main-auxiliary-standby-maintenance to run, and main process equipment is in closed loop control state all the time.

4. an air compressor monitoring and diagnosis method for self-adaptive kernel gauss hybrid models, is characterized in that: adopt arbitrary monitoring and diagnosis system in 1-3, concrete steps are as follows:

(1) determine the key variables that fault diagnosis is used, gather air compressor sample data as training sample;

Monitoring parameter used comprises: the voltage of pump motor, electric current, working time; Axle temperature, working time after axle temperature, rotor before the voltage of dragging motor, electric current, stator axle temperature, rotor; Pressure in bellows chamber, temperature; The intake pressure of air compressor, discharge pressure, entering water temp, water-exit temperature;

(2) being normalized collecting collection air compressor sample data, data being removed the impact of dimension;

(3) in low n-dimensional subspace n, GMM is used to disclose data to cluster data multi-modal;

(4) then according to data multi-modal information, the kernel functional parameter algorithm for estimating based on entropy is utilized to find local optimum kernel functional parameter in original data space;

(5) local optimum kernel functional parameter is utilized to use KPCA that non-linear higher-dimension multi-modal data set transformation low-dimensional is differentiated subspace, if algorithm does not reach end condition, then forward the first step to and continue iteration execution, complete the fault diagnosis to air compressor system by self-adaptive kernel gauss hybrid models.